Method and apparatus for transducer temperature compensation

ABSTRACT

Method and apparatus for compensating a position servomechanism for errors introduced by differences in coefficients of thermal expansion between a transducer element and a positioned element. A position displacement signal based on distance from a center position on the transducer element and a temperature variation signal based on the difference between the ambient temperature and a reference temperature are multiplied together with appropriate constants to generate an error signal which is applied to the servomechanism to correct the final position.

United States Patent [1 Du van 4] METHOD AND APPARATUS FOR TRANSDUCER TEMPERATURE COMPENSATION [75] Inventor: Wilbur E. Du Vall, Redondo Beach,

A Calif.

[73] Assignee: Xerox Corporation, Rochester, NY.

[22] Filed: Sept. 15, 1972 21 Appl. No.: 289,447 r [52] US. Cl..' 318/634, 33/125, 77/5 [51] Int. Cl. .A G05d 23/275 [58] Field of Search 318/634; 33/125;

{561 References Cited 7 UNITED STATES PATENTS 3,142,120 7/1964 Mottu 33/125 3,236,124 2/1966 Rhoades 7/1967 Loewen 1 Nov. 27, 1973 3,579,073 5/1971 Johnstone 318/634 2,844,775 7/1958 Miller et al.

3,527,991 9/1970 Sackin 3,646,839 3/1972 Shillam 318/634 X Primary Examiner-B. Dobeck Attorney-James J. Ralabate et a1.

57 ABSTRACT 13 Claims, 5 Drawing Figures 1 "F.7d H" COMM/1 NDED p05/r/0/v5/6. 457M709 r 5*, I GENE? Ta I t A I l j i I 32 I 4 I l 1 30 1/54 00/71 1 i 2590 -l/A 007 i SEA/s02 TflWififlCEkT 1 42 I 26 1 1 26 75 25 I fl05/ r/oA 1 cow/ 271 92702 Kart 50am I I i 42 46 7/ J 1 26 TEMPAAT/EE 1 rem 500cm :"36

r 1* METHOD-AND APPARATUS FOR TRANSDUCER TEMPERATURE COMPENSATION BACKGROUND OF THE INVENTION The present invention relatesgenerally to temperature compensating systems and, moreparticularly, to systems for correctingposition servomechanisms for ambient temperature fluctuations.

' In the field of magnetic disc memory: systems, precision position servornechanism are commonlyemployed to position a magnetichead overaparticulantracle'on' the disc. In such systems, relatively high' resolution po sition transducers are needed and a commonly used transducer incorporates a pair of optical gratings; one fixed and one moveable with the carriagefor the magnetic heads. A beam of light is passed through the gratings toaphotocell. Relative movement of thegratings produces recurrent light fluctuations which are detected by the photocell and counted as an indication of thepo'sition of the moveable grating and carriage. Typically, the positioning of a head over a particular track is referenced to a particular countassociated with a particular physical position along the moveable optical grating.

Theoptical gratings used with such transducers are i normally constructed of glass or thelik'e' which has a different coefficient of thermal expansion than the metal used in the carriage. Temperature variations then: cause the head to be, positioned in a different'place than that indicatd by the position transducer. Thus,r-if

ture. varied. However, as the spacing between tracks decreases, the accuracy of these prior techniques becomes inadequate for practical use.

Thus, there has long been a need for a reliable and accurate temperature compensating technique which insures the proper positioning of an element, such as a magnetic head, despite variations in the ambient temperature. The present invention satisfies that'need.

SUMMARY OF THE INVENTION The present invention provides a method and apparatus for temperature compensation of positioning system so that an element, such as a magnetic head, may

be reliably and accurately positioned despite variations in the ambient operating temperature and differences between the coefficients of thermal expansionof the positioned element and the position transducer elements. I

In the system of the invention, the position error isa function of position along a moveable transducer element and the ambient temperatureJTherefore, a position transducer signal is combined with a temperature signal to generate an'error signal'which is then'applied to the positioning system to cause a corrective'movement of the positioned element. In the presefltly-preferred embodiment of the invention, the error signalis selectively applied tothe positioning system only when the positioned element is at rest at an app'arentcommanded position. The error-signal is then applied to the positioning system to cause the position'ed element to be moved to the correctedposition: Thus, theztemperaturecompensating system does not interfe're with the" conventional operation of the positioning system:

When "a new it commanded "position is desired, the error".

signal is disconnected from the positioning system whilethe positioned element'is moved to its new position;

In the position trahsducerusedinthe presently"pre ferred embodiment of'theinvention'; an optical grating: is mounted" on the carriage and ?moves: with I it past i a-= fixed 'optica] grating and i associated light source and i photocell The moveableopticalgrating is mounted substantiallyatftheficenterof its length leavinga th'elends free. The, center mountingzi point is then temperature invariant with "respect "to the carriage and heads while the ends 'may expandbr contract with variations in the ambienttemperature. I

There is'an= exact correspondence between the position signal produced by rthe' position transducer and the actual head position foronl-y o'nerefrence temperature; For other" ambientitemperatures, the positionerror-is dependent on the distance, plus or minus,-along the moveable grating fromthe center mounting" point (position displacement) and thedifference, plus orminus, between-"the ambienttemperature andithe' refer= ence' temperature (temperature van'ation)..

In thesystem ofthe: invention, an error signal is generated which is proportional to the product of the position displacementandthetemperature variation;- The multiplication is-accomplished by suitable electronic circuitry and-'the-error-signal is applied to the input-of a position servomechanism' resultingin a'corrective movement of the carriage and heads.

Thus; the presentwinvention provides a temperature compensatingcsystem for use'with a positioning system having positioned elementsandposition transducer 'elements-with different coefficients of thermal expansion; The-generatederrorsignal is highly accurate in that itis dependent on bothposition on the transducer itself andtemperature variationz Other features and'advantages of thepresent invention will'become apparent from the following detailed'd'escription of the presently preferred embodiment.:

BRIEF DESCRIPTION OFTHE DRAWINGS FIG. 1 is a block diagram of a position servomechanism incorporating thetemperature compensating system of the present invention;

FIG? 2"is acombined block diagram and electrical schematic diagram of "a presently preferred embodiment of'a circuit for generating the error signal;

FIG.- 3 is a diagrammatic perspective'view of'an opti-v cal grating position transducer;

"FIG.'4"isagraph1ofa waveform of the output signal from the photosensor used with'the optical grating'position' transducer; and' FIG. 5"is' a graphof a detail of the'waveform of FIG. 4-illustrating me effect of the addition of "the error sig-= nali DESCRIPTION OF- THE PREFERRED EMBQDIMENTv Turning 'now to the'drawings, andzparticularly-FIG.

l:thereof, the temperature compensating system: of the present invention is utilized in a magnetic disc memory system in which a magnetic head is positioned on the surface of a magnetic disc 12 by means of a position servomechanism 13, including an electromechanical actuator 14 The actuator 14 is of conventional design and is driven by an amplifier 16 which receives a control signal on a line 18 which is the result of a number of signals appearing at a summing junction 20. Typically, the control Signal applied to amplifier 16 is basically the difference between the signal on line 22 from a commanded position signal generator 24and a present position signal on a line 26 from a position transducer 28. Typically, in such a position servomechanism 13, an additional velocity signal on a line 30 from a velocity transducer 32 is included in the control signal to improve stability. The position transducer 28 and velocity transducer 32 are mechanically connected, as illustrated by dotted line 34, to the positioned element, or carriage, on which the head 10 is mounted.

conventionally, when the head 10 is in its proper or commanded position, the sum of the signals in the summing junction -results in a zero control signal as input to amplifier 16. It should be appreciated that the position servomechanism 13 forms no part of the present invention and the design and construction of such systems is well known to those skilled in the art.

The temperature compensating system 36 of the present invention provides an additional input on a line 38 to the summing junction 20. The error signal on line 38 is selectively applied to the summing junction 20 by means of ,a switch 40 when the head 10 is at rest on an apparently correct position. The position servomechanism 13 then functions normally when moving between commanded positions. Any conventional means such as a zero velocity sensor 42 determines when the head 10 is at rest and controls the operation of the switch 40. The switch 40 and zero velocity sensor 42 areof conventional design and may be implemented by techniques well known to those skilled in the art.

The error signal on line 38is a function of the indicated present position signal on line 26 from the position transducer 28 and the ambient temperature indicated by a temperature signal on line 44 from a temperature transducer 46 preferably in the vicinity of the position transducer 28 to follow changes in ambient temperatures near the transducer. The position signal on line 26 and temperature signal on line 44 are combined in a temperature compensator 48 which generates the error signal on line 38 which is applied to the summing junction 20 to reposition the head 10 on the magnetic disc 12.

While the temperature compensating system of the present invention may be utilized with any type of position transducer 28, the presently preferred embodiment of the invention was designed for use with an optical grating position transducer such as that illustrated in FIG. 3. Typically, such a position transducer includes a light source 50 which directs a beam 52 of light througha moveable optical grating'54 which is physically attached to a carriage 56 on which the head 10 (FIG. 1) is mounted. The beam 52 passes through the moveable optical grating 54 and then through a stationary optical grating 58 and a photosensor 60. Movement of the optical grating 54 past the stationary optical grating 58 causes fluctuations in the beam 52 of light reaching the photosensor 60 which are conventionally electronically processed to provide an indication in the position of the carriage 5.6 and head v10.

cate the track number. Thus, in FIG. 2 the counted In the particular optical grating position transducer used in the presently preferred embodiment of the invention, the output of-the photosensor 60 is substantially a sine wave such as that illustrated in FIG. 4. The spacing between the lines on the moveable and stationary optical gratings 54 and 58, respectively, is such that a complete cycle is generated for each track on the magnetic disc 12. The sensing circuitry is such that proper position of the head 10 on a track is indicated as the waveform passes through a zero reference voltage on the positive going portion of the wave. The number of zero crossings is conventionally counted during movement of the carriage 56 to indicate with which track the head is aligned.

The servomechanism 13 is designed so that the head 10 is stopped when the output of the photosensor 60 is at the commanded track (n) of N possible tracks with the final exact position being determined by the output of the photosensor being at the zero reference voltage on the positive going side of the waveform. Again, the implementation of a servomechanism 13 for effecting this operation forms no part of the present invention and the design of such systems iswell known to those skilled in the art.

The servomechanism 13 moves the carriage 56, the head 10 and the moveable optical grating 54 to a position which results in a zero crossing output of the photosensor 60 for a particular desired track number. However, because of different coefficients of thermal expansion of the grating 54, and carriage 56, the correspondence between the head 10 position and grating 54 position will be correct for only one particular reference temperature. As the ambient temperature varies from the reference temperature, the moveable optical grating 54 expands or contracts more or less than the carriage 56 and head 10 depending upon their respective thermal coefficients of expansion. Thus, when the servomechanism 13 is at rest and the output of the photosensor 60 is at zero, the actual position of the head 10 may not be correct.

The temperature compensating system 36 of the present invention generates an error signal e which, as illustrated in FIG. 5, has the effect of adding or subtracting a fixed voltage to the position transducer waveform. The position servomechanism 13 then seeks a combined error signal e and photosensor 60 output which results in a new effective zero crossing at 61. This in turn causes corrective movement of the moveable optical grating 54 and the head 10 by a small distance Ax to the correct track location. 7

It should be noted that the addition of the error signal e essentially follows the non-linear sine curve but that the error signals e are generally small and the corrections normally take place over the substantially linear region of the curve around the zero'crossing point. If

larger corrections are contemplated in which the effect of the non-linearity would be significant, an optical grating system which produces a more triangular waveform may be employed.

The correction signal 2 may be generated by any conventional circuitry well known to those skilled in the. art. An example of such circuitry is illustrated in FIG. 2. As discussed above, the position transducer 28 essentially produces a sine wave in which positive going zero crossings are indicative of a track position the number of such zero crossings being counted to indivs zero crossings. from the position transducer 28' are stored in a position transducer register 62. The stored number in register 62 indicates position as a track number (n) over which the head is apparently, positioned. The digital position-,signal in register 62 is applied to a digital-to-analog converter 64-to generate an analog position signal voltage V which generally, is of the form: V =-K n where K is a suitable constant for the particular circuitry.

As discussed above, the correction signal is dependent upon the distance from the center point of the moveable optical grating 54 and a reference voltage V 7 tors R1, toa summing point. providinga voltage V indicative of the distance, positive or negative of the' moveable opticalgrating 54 from its center point or position displacement V has the form Y KAN-n) where K again is a suitable constant. v

The signal voltage V is connected through resistors R2 and R4 to the positive and negative inputs, respectively, of an operational amplifier 68. A temperature sensitive resistor R3 is also connected between the positive input to the operational amplifier 68 and a reference ground. The configuration-of resistor R3 is such that resistance changes-are proportional to the difference between a reference temperature (T,.) and the ambient temperature (T) or AR3 k R T,T) where k is a combined coefficient of thermal expansion for the complete system and R is the reference resistance for R3.

The negative input of operational amplifier 68 is also connected to ground through a resistor R5. The output of the operational amplifier is the correction signal e and feedback from the output of the amplifier to the negative input is provided by. a resistor R6. The resistance networks at the inputs to the operational amplifier are such that 'when the temperature sensitive resistor R3 is at a reference temperature (7",), the error voltage e is zero. Variations in the ambient temperature then cause the error signal e to be positive or negative depending on the direction of temperature change.

Generally, the error voltage e has the form where K, is ,the total systemconstant which can be shown to be It should be appreciated that the circuit shown in FIG. 2 is only one example and that many circuit variations are possible for any particular positioning system. Thus theonly requirement for the error signal e is that it be proportional to both position displacement and temperature variation and suitable constants are added: depending on the particular system. While a particular technique for utilizing the error signal has been described, it should be appreciated that many modifications are possible in order to utilize. the temperature compensating technique of the invention in a different positioning system. Thus, the scope of the temperature compensating system of the invention is not intended to be limited except by the following claims.

I claim:

l. A temperature compensating system for use in a positioning system having 'aposition transducer element moveable with a positioned element, said transducer element having a different coefficient of thermal expansion than said positioned element, said temperature compensating system comprising:

means for sensing the position of said transducer element and generating a position signal;

means for sensing the ambient temperature around said transducer element and said positioned element and generating a temperature signal;

means for combining said position signal and said temperature signal to generate an error signal dependent upon the difference in expansion of said position transducer element and said positioned element due to variation of said ambient temperature; and I means for applying said error signal to said positioning system- I i v 2. A temperature compensating system as defined in claim 1 wherein:

said combining means multiplies said position signal by said temperature signal and appropriate constants to generate said error signal which is depen- -dent upon the position of said transducer element and said ambient'temperature. v

3. A temperature'compensating systemas defined in claim 1 wherein'said means for sensing ambient temperature includes:

means for comparing said ambient temperature with a reference temperatureto generate a temperature variation signal indicative of their difference.

4'. A temperature compensating system as defined in claim 1 wherein:

said means for position sensing includes means for comparing the sensed position with a midpoint along the length of said transducer element to generate a position displacement signal indicative of the distance and direction from that midpoint; said means for sensing ambient temperature includes means for comparing said ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature; and

' said combining means multiplies said position signal by said temperature signal and appropriate constants to generate said error signal.

5. For use in a position servo-mechanism having a positioned element, a temperature compensating system.

comprising: v 7

an optical grating position transducer having an'element moveable with said positioned element, the

physical position of said moveable transducerelei a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature; means for multiplying said position signal by said temperature variation signal and appropriate constants to generate an error signal; and

means for applying said error signal to said position servomechanism to cause corrective movement of said positioned element.

6. For use in a position servomechanism having a positioned element, a temperature compensating system comprising:

an optical gratingposition transducer having an element moveable with said positioned element, said moveable transducer element being mounted at a midpoint along its length, the physical position of 1 said moveable transducer element being indicative of the physical position of said positioned element, said moveable transducer element having a different coefficient of thermal expansion'than said positioned element; i g 1 means for sensing the position of said moveable transducer element and generating a position signal, said means for sensing compares the sensed position with said midpoint to generate a position displacement signal indicative of the distance and direction from that midpoint; means for comparing ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature;

means for multiplying said position displacement signal bysaid temperature variation signal to generate an error signal; and

means for applying said error signal to said position servomechanism to cause corrective movement of said positioned element.

7. A temperature compensating system as defined in claim 6 wherein:

said means for applying selectively applies said error signal to said position servomechanism when said positioned element is at rest on an apparent commanded position.

8. A temperature compensating system as defined in claim wherein:

said means for applying selectively applies said error I signal to said position servomechanism when said positioned element is at rest on an apparent commanded position. 9. A method of temperature compensating a positioning system which has a position transducer element moveable with a positioned element with the transducer element having a different coefficient of thermal expansion than said positioned element, said method of temperature compensating comprising the steps of:

. combining said position signal and said temperature signal to generate an error signal dependent upon the difference in expansion of said position transducer element and said positioned element .due to variation in said ambient temperature; and

applying said error signal to said positioning system.

10. The method defined in claim 9 wherein:

said combining step includes multiplying said position signal by said temperature signal and appropriate constants in order to generate a said error signal; and

said temperature sensing step includes comparing said ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature.

11. The method defined in claim 9 wherein:

said'applying step includes selectively applying said error signal to'said positioning system when said positioned element is at rest on an apparent commanded position. 12. A temperature compensating system for use in a position servomechanism for positioning a magnetic head over a desired track, the magnetic head and associated carriage moveable with the moveable element of an optical grating position transducer; said moveable transducer element having a different coefficient of thermal expansion than said magnetic head and associated carriage, said temperature compensating system comprising: 7

means for mounting said moveable transducer element on said carriage at a midpoint along the length of said element, the ends of said element being free for thermal expansion and contraction;

means for comparing the sensed position of said moveable transducer element with said midpoint and generating a position displacement signal indicative of the distance and direction of movement from that midpoint; means for comparing ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature; means for multiplying said position displacement signal by said temperature variation signal and appropriate constants to generate an error signal; and

means for selectively applying said error signal to said position servomechanism whensaid carriage and magnetic head are at rest at an apparent commanded position to cause corrective movement of said head. 13. A method of temperature compensating a positioning system which has a position transducer element moveable with a positioned element with said transducer element having a different coefficient of thermal expansion than said positioned element, said method of temperature compensating comprising the steps of:

mounting a moveable element of an optical grating position transducer for movement with said positioned element, said moveable transducer element being mounted at a midpoint along its length;

sensing the position of said transducer element and comparing the sensed position of said moveable element with said midpoint to generate a position displacement signal indicative of the distance and direction from said midpoint;

sensing the ambient temperature and generating a temperature signal in response thereto;

combining said position signal and said temperature signal to generate an error signal; and

selectively applying said error-signal to said positioning system when said positioned element is at rest on an apparent commanded position to compensate for variations in ambient temperature.

$22253? UNITED STATES PATENT 01 mg ,v v I CERTIFICATE 01 CORRECTION Peteet No. 17751 5 Dazed November 27 1973 Inventoflsy wllbur E. Du Vall V It is eertified that error appears in the aboveidentified patent and that said Letters Patent are hereby corrected as shown below:

H 1 Column 3, therefor --to---. v

Column 5, line 50', delete "t" and insert the'refor''I line- 51 delete "K and insert therefor line 62, delete "and" and insert Signed a sealed this 23rd day of" Apr l 197E.

" (SEAL) Attest:

EDWARD 'I/LFLETCHERJR. V CpMARSfiALL DANN Attesting Officer Commissioner of Patents mg UNITED STATES PATENT OFFICE CERTIFICATE 0E CORRECTION Patent 3,775,655 Dated November 27, 1973 Inventor). Wilbur E. Du v It: is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

F '1 Column 3, line 62, delete "and" and insert therefor to--.

Column 5, line 50, delete "t" and insert therefor 'I line 51 delete "K and insert therefor Signed and. sealed this 23rd day of April 197E.

(SEAL) Attest:

EDWARD II.FLE'ICEIER,JR C. MARSHALL DANN Attesting Officer Commissioner of Patents 

1. A temperature compensating system for use in a positioning system having a position transducer element moveable with a positioned element, said transducer element having a different coefficient of thermal expansion than said positioned element, said temperature compensating system comprising: means for sensing the position of said transducer element and generating a position signal; means for sensing the ambient temperature around said transducer element and said positioned element and generating a temperature signal; means for combining said position signal and said temperature signal to generate an error signal dependent upon the difference in expansion of said position transducer element and said positioned element due to variation of said ambient temperature; and means for applying said error signal to said positioning system.
 2. A temperature compensating system as defined in claim 1 wherein: said combining means multiplies said position signal by said temperature signal and appropriate constants to generate said error signal which is dependent upon the position of said transducer element and said ambient temperature.
 3. A temperature compensating system as defined in claim 1 wherein said means for sensing ambient temperature includes: means for comparing said ambient temperature with a reference temperature to generate a temperature variation signal indicative of their difference.
 4. A temperature compensating system as defined in claim 1 wherein: said means for position sensing includes means for comparing the sensed position with a midpoint along the length of said transducer element to generate a position displacement signal indicative of the distance and direction from that midpoint; said means for sensing ambient temperature includes means for comparing said ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature; and said combining means multiplies said position signal by said temperature signal and appropriate constants to generate said error signal.
 5. For use in a position servo-mechanism having a positioned element, a temperature compensating system comprising: an optical grating position transducer having an element moveable with said positioned element, the physical position of said moveable transducer element being indicative of the physical position of said positioned element, said moveable transducer element having a different coefficient of thermal expansion than said positioned element; means for sensing the position of said moveable transducer element and generating a position signal; means for comparing the ambient temperature around said transducer element and said positioned element with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature; means for multiplying said position signal by said temperature variation signal and appropriate constants to generate an error signal; and means for applying said error signal to said position servomechanism to cause corrective movement of said positioned element.
 6. For use in a position servomechanism having a positioned element, a temperature compensating system comprising: an optical grating position transducer having an element moveable with said positioned element, said moveable transducer element being mounted at a midpoint along its length, the physical position of said moveable transducer element being indicative of the physical position of said positioned element, said moveable transducer element having a different coefficient of thermal expansion than said positioned element; means for sensing the position of said moveable transducer element and generating a position signal, said means for sensing compares the sensed position with said midpoint to generate a position displacement signal indicative of the distance and direction from that midpoint; means for comparing ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature; means for multiplying said position displacement signal by said temperature variation signal to generate an error signal; and means for applying said error signal to said position servomechanism to cause corrective movement of said positioned element.
 7. A temperature compensating system as defined in claim 6 wherein: said means for applying selectively applies said error signal to said position servomechanism when said positioned element is at rest on an apparent commanded position.
 8. A temperature compensating system as defined in claim 5 wherein: said means for applying selectively applies said error signal to said position servomechanism when said positioned element is at rest on an apparent commanded position.
 9. A method of temperature compensating a positioning system which has a position transducer element moveable with a positioned element with the transducer element having a different coefficient of thermal expansion than said positioned element, said method of temperature compensating comprising the steps of: sensing the position of said transducer element and generating a position signal in respOnse thereto; sensing the ambient temperature around said position transducer element and said positioned element, and generating a temperature signal in response thereto; combining said position signal and said temperature signal to generate an error signal dependent upon the difference in expansion of said position transducer element and said positioned element due to variation in said ambient temperature; and applying said error signal to said positioning system.
 10. The method defined in claim 9 wherein: said combining step includes multiplying said position signal by said temperature signal and appropriate constants in order to generate a said error signal; and said temperature sensing step includes comparing said ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature.
 11. The method defined in claim 9 wherein: said applying step includes selectively applying said error signal to said positioning system when said positioned element is at rest on an apparent commanded position.
 12. A temperature compensating system for use in a position servomechanism for positioning a magnetic head over a desired track, the magnetic head and associated carriage moveable with the moveable element of an optical grating position transducer, said moveable transducer element having a different coefficient of thermal expansion than said magnetic head and associated carriage, said temperature compensating system comprising: means for mounting said moveable transducer element on said carriage at a midpoint along the length of said element, the ends of said element being free for thermal expansion and contraction; means for comparing the sensed position of said moveable transducer element with said midpoint and generating a position displacement signal indicative of the distance and direction of movement from that midpoint; means for comparing ambient temperature with a reference temperature to generate a temperature variation signal indicative of the difference between said ambient temperature and said reference temperature; means for multiplying said position displacement signal by said temperature variation signal and appropriate constants to generate an error signal; and means for selectively applying said error signal to said position servomechanism when said carriage and magnetic head are at rest at an apparent commanded position to cause corrective movement of said head.
 13. A method of temperature compensating a positioning system which has a position transducer element moveable with a positioned element with said transducer element having a different coefficient of thermal expansion than said positioned element, said method of temperature compensating comprising the steps of: mounting a moveable element of an optical grating position transducer for movement with said positioned element, said moveable transducer element being mounted at a midpoint along its length; sensing the position of said transducer element and comparing the sensed position of said moveable element with said midpoint to generate a position displacement signal indicative of the distance and direction from said midpoint; sensing the ambient temperature and generating a temperature signal in response thereto; combining said position signal and said temperature signal to generate an error signal; and selectively applying said error signal to said positioning system when said positioned element is at rest on an apparent commanded position to compensate for variations in ambient temperature. 